Educational apparatus



March 13, 1928.

1,662,272 P. E. K'LOPSTEG anucATloriAL APPARATUS Filed Feb. 20. 1926 1 2 Sheets-Sheet 1 P ZTKZO" March 13, 1928. 2 1,662,272

P. E. KLOPSTEG EDUCATIONAL APPARATUS Filed Feb. 20, 1926 2 Sheets-Sheet 2 3K 19 -H? mill/17% My v 6 7 9 70 "Zia/@7071)? Patented Mar. 13, i 1928.

UNITED STATESPATENT OFFICE.

PAUL E. KLOISTEG, OF CHICAGO, ILLINOIS, ASSIGNOR TO CENTRAL SCIENTIFIC COH- PANY, OF CHICAGO, ILLINOIS, A CORPORATION OF ILLINOIS. I

EDUCATIONAL APPARATUS.

Application filed February 20, 1926. Serial No. 89,651.

' This inventionrelates to laboratory apparatus of the type used in teaching physics and. has for its principal objects to provide apparatus simple enough for the ordinary student to readily understand and yet capable of accurately demonstrating the relation between centripetal force and the mass, angular velocity and the radius of the path of a rotating body, usually expressed by the equation f=mw r to permit the rotating body to be maintained in a condition of equilibrium under the balanced action of centrifugal and centripetal forces; and to permit the resistance to outward movement representing centripetal force to be increased with the increase of radius of rotation.

Instructors in physics have been hampered in making illustrative experiments to demonstrate this simplerelationship because the apparatus available is not well suitedfor the purpose. Those forms which are sulficiently simple for the student to use are incapable of giving data sufficiently close to the computed values to make the desired impression upon the students' mind, and those forms which are intended for accurate work are so complicated in design and construction and so obscure in their operation that the student is impressed with the inability of mechanical science to approach mathematical accuracy rather than the lesson which it is intended to teach by the experiment.

In most of the simple forms centripetal force is supplied by weight which, of course, has a constant value, and in approaching the angular velocity at which the weight is balanced by the centrifugal reaction of the rotated mass, the radius of rotation of the latter increases, slightly increasing the centrifugal force, and throwing the apparatus out of balance in the opposite direction. As :1 result, in order to mamtain the condition of average equilibrium it is necessary to vary the rotational speed above and below that point at which theoretical balance is obtained. Or if there is apparent equilibrium at constant speed the stabilization is the retrated in the accompanying drawings in p Fig. 1 is a perspective View illustrating the preferred form mounted upon a conventional rotator; a

Fig. 2 is a front elevation of the'preferred form of a commercial unit, the ends thereof being in longitudinal section on a vertical. plane; I Fig. 3 is a transverse section on the line 3-3 of Fig. 2; p

Fig. 4 is an end View looking from the. left in Figs. land 2; p

Fig. 5 is an elevation of the preferred form suspended from the support and. sub jected to weights for measuring the values:

required for equilibrium;

Fig. 6 is aside elevation of an. alternative form of commercial unit;

Fig. 7 isa transverse sectional view thereof on the line 7 -7 of Fig. 6;, r i

Fig. 8 is a diagrammatic View illustrating an alternative embodiment, and 1 Fig. 9 is a diagram illustrating the forces developed in the spring during rotation of the apparatus.

These specific illustrations and the correspondingly specific description which follows are used to make the disclosure full and clear, and it is not intended by either of themto limit the scopeof the claims other than is made necessary by the prior art.

The commercial unit capable of use with various forms of rotators includes a generally rectangular, frame A comprising a top 10, bottom 11, and ends 12 and l3,,made as have been had with a frame of thin aluminum equipped with a transversely arrangedpin 19 (Fig. 2) projecting from the bottom and adapted to be received and secured in a socket (Fig. 1) of a variable speed rotator generally indicated by B.

A cylindrical mass 14; is equipped with a pin 15 (Fig. 3) mounted upon pivot bearlugs 16 carried by arms 1? on the bottom 11 of the frame. The pin 15 is necessarily at one side of the center of gravity of the mass and when the pivotal axis is practically tangential to the mass, as shown, ample movement of the center of the mass is permitted, which movement is limited by end 13 of the frame and by an upright stop 18 on the top 10.

Outward movement of the mass 1-1 under the action ti centrifugal force is resisted by a. helical spring 21 with its axis in line with the center of gravity of the mass M and having one end hooked through an eye 22 mounted at the axis of the inner face of the mass 11 and the other end engaged With a hook 2% (Fig. 52) mounted at the center of the plug 25 bearing against the end of the threaded sleeve :26 adjustably mounted in the threaded partition .27 adjacent to the end 12.

Dynamic balance is etl'ectcd by a cylindrical counter weight 28 located between the partition 27 and the end 12 and secured to the latter by screws 29 and having a central opening 30 to accommodate the plug 25 in the outer end of the sleeve 26.

The intern'iediate portion of the ends 12 and 13 are circular as indicated at 31 in Fig. 4, to conform with the shape of the mass 1% and the counterweight 28, but the top and bottom are relatively narrow to conform with the remote portions of the ends, as indicated at 32 and 33, in Fig. 4.

The condition with respect to equilibrium is indicated by a pointer 31 carried by the mass 1- and an index button 35 having a narrow head, and mounted coaxial with the stem 19.

The mass let is provided with a circumferential line 36 in the plane of the center of gravity of the mass and the top 10 is provided with a. line 37 in the plane of the axis of rotation and the distance between the points where these planes cut the axis of the -spring represents the radius of rotation, which is easily measured with Vernier calipers.

Both the ends 13 and 12 are perforated, as indicated at 38 and 39. The latter is bridged by a loop 40 secured to the end 12 by the screws 29. The opening 238 permits access to an eye all secured to the mass 1% in line with the center of gravity.

By means of the loop 40 and a. suitable hanger 12 (Fig. the frame with its associated parts may be suspended from a support -13. By means of the eye 41 and line wire 44-, a weight carrier 4-5 may be suspended below the mass 14.

The rotator B includes a source of power 4.6 for driving a shaft 17 which is connected with a. vertical shalt 4.8 by friction gearing 49, 50, and the upper end of this shai l; carries the socket 2U equipped with a set screw 51 for securing the stem 19 in the socket. A counter 52, carried by a spring 53. has a. gear at normally held out of engagement with a gear 55 on the socket Qt).

A fork 56 has a threaded hub mounted on the screw 58 equipped with a knurled knob 59 permit l ing the friction gearing to be adjusted to vary the speed of the shalt -18 and, hence, the frame A.

The use of the apparatus is illustrated in Figs. 1 and When it is desired to pcr- T'Olli'l the experiment the assembly shown in Fig. 1 set in motion and by means of the knob 59 the speed of the frame A is adjusted until the sharp end of the poinlcr 2H is opposite to the =-.harp edge of the index 35. This condition of: balance is shown in the figure.

Having noted the reading of the revolution counter it is engaged with the rotator spindle at a definite instant and the number of revolutions in dclluite intervals of time are noted. Iii, during the taking of a. reading, the pointer 3-1 moves, it is an iiidicalion that the speed of the n'iotor is varying and the knob 59 should be turned to compensale for the variation. The construction shown in the drawing is so designed as to be very sensitive to small changes in the speed and it is, therefore, not dillieult to obtain values for the number of revolutions in one minute intervals which agree within one or two revolutions.

This part of theexperiment having been completed the stem 19 is withdrawn from the socket and the frame It is suspended, as indicated in Fig. \Veights (30 are placed on the carrier -15 until the pointer 34 indicates a balance, as it did during the rotation of the apparatus, as shown in Fig. 1. Having determined the weight, including that of the mass ll, necessary to pull the spring to the point of balance, the radius of rotation is measured by a vernicr caliper between the lines 36 and 37, which completes the data for the calculations.

It may he observed at this point that suspending the apparatus and weights in the manner shown the axis of the spring is automatically placed in vcilical position, which is a i'iecessary condition for accuracy in measuring directly the pull of the spring.

It is also opportune to note that by using;- a spring to exert the cenlri 'ielal force an increase of radius of rotation oi" the mass effects an elongation of the spring and. consequently, increases the centripetal tori-c simultaneously with the increase oi i-enlrr fugal force due to the lengthening of th radius. The relative rate at. which ea -h of these forces shall increase with an increase Bil Ion

of radius (but at constant speed) may be predetermined by appropriate proportioning of the parts. If the rates of increase are made equal a condition of such critical equilibrium is set up that the slightest increase in speed throws the balance in favor of centrifugal force, while the slightest dc crease throws the balance in tavorof centripetal force.

in the region of balance.

If, however, the increase of centripetal force with radius, at the predetermined F,, F or E0 Mw r (Eql) cZF a? C,s1nce C 7* (Eq. 2) (1F dr =Mw (Eq. 3)

Equations (2) and (3) represent the respective rates of increase, with radius, of the centripetal and centrifugal forces. If these are to be equal, a

'0 M002 (Eq. 4

But (1) must be true simultaneously; hence, if we solve (2) and (4t) simultaneously we have E =7" (Eq. 5).

Equations (4:) and (5) constitute the basis for the design. We note that we can attain the condition of stability, yet maintaining great sensitiveness to changes in speed, by making C slightly larger than Me Eq. (5) shows that a spring, in order to give the results sought, must, at the condition of balance expressed in Eq. (1) be elongated an amount equal to the distance of the center of mass A from the axis.

The tension adjustment for the spring 31 is provided to enable the student to test the equation at several different values oi the forces. It should be noted that at lower values of the tension than maximum, at

which the critical condition is approached,

the apparatus becomes less sensitive to speed variations; however, it i" amply sensitive to permit accurate agreement among successive measurements of revolutions per minute.

The correction to hlw 'f' resulting from the This would make the device excessively sensitive to changes in speed fact that, on account of the mass of the spring, the latter elongates slightly during rotation, may be readily determined. At first thought it might seem that, since the two halves are approximately symmetrical about the axis, each is pulling outward with a force Where m is the total mass and 21" the total length of the spring, so that the elongation might be expected to correspond to twice this force or mw r/2. .That the elongation, and consequently the additive correction to F as computed from Me r, is less than this amount will appear from the following analysis: p

In the diagram Fig. 9, let the Y -axis rep resent the axis of rotation, and assume that the spring is close-wound. The following designations will be used: f

r length of helix, axis of rotation to free end- (approximately true, as required by Eq. 5)

5 mass of spring from axis to end center of wire a number of turns per cm..

(p =torsionalcoefficient, i. e., angle of twist per unit length of wire per unit torsional moment.

0 elongation in cm. i

The torqueon any cross section of wire,

at the point P, a distance a; from the axis, is" that winch results from the centrifugal force of the mass beyond P from the axis. This mass. is

and the center of mass'of this portion is located-at (Fred/2. The force, which acts along the axis 01 the spring, acts with a moment in which the lever arm isa. Hence the torque on the wire at P is s nd) nine? In a length of wire included within the distance also, namely 2 a ads the angle of twist (it) produced by the torque t is ow o and C arerelated bythe formula and the elongation e is the product of the a 'radius of coil, from axis of cylinder to ion lltl

twist in the entire length of wire comprising the spring, and the radius of the turns. Hence we may write The force corresponding to this elongation is Co, and twice this force is the correction to be added to Bi r. because the same clonnation occurs in each half of the spring thus,

Finally, the equation for the total force. with the spring correction included lS l Exni', a en mediminillill mum tension tension of l of spring.

man-

tension ttlnailts spring.

196.4 19 3.4 195.5 A change in M was between Exps. 2 and K.

(52* Av "12 VilllliS of 3 1' urements in M (rotating mass). a

r (radius. axis to 5.70 are center of mass) cm. e .1 case.

. mmtk) 50.6 51.5 an Average R. l. M. 1 found from number of revolutions (luri in five 1-minute intervals. 1n(massol'sprlngrlm 12.0 12,0 1" FE, prams, (coin- .iT-tt) T3080 '7 La t ingure rounded.

outed from (11+ in La r 3 y Observed F... eenarm that) 1100 Apparatus sensitive toilO grams. erred bysprimz.

tripeial force ex- In Fig. (3 there is shown an alternative arrangement of the centrifugal mass and pointer. The mass ()1 corresponding to the mass l-linstead of being pivoted. is slidably mounted between the three rods '2, extending between the end piece (33 and a lug (3-1. on the top 65, and lugs 66 on the bottom 6?.

The bottom 6? is split at; 68 and a pointer 05 is pivoted at 70 and provided with a short arm 71 lying in the path of the mass 61 as it moves outwardly under centrifugal force. The weight of the pointer together with centrifugal force normally tend to give it av colmter-clockwise rotation in imposition to the action of the mass 01.

In Fig. 8 the frame AA is provided with a lateral extension 72 in which the spring 73 is mounted on an axis coin tant with the axis of rotation. and the flee end of the spring is connected with the mans Tl by a llcxible able T5 whine direction changed from vertical to horizontal by a rotating lever illustrated by the circular sheave T6. In this form the correction for the spring, as developed in the (ll -(l l ll|'t. becomes unnecessary, beeanrc the axis of the wring substan tially coincides with the axis of rotation. The poss'ibilit. of error in measuring the force by apptvine weights is increastal. howerer. became of fiat-t ion in the rotating lever used to transmit. the form. through av right angle.

ln all fornn of the apparatus the mass rlltllllil be of simple regular gz'eometrie form to facilitate the accurate In anion ol' the center of mass.

I claim as my invention:

l. in a centrifugal instruction device. a rotating support, a mass of simple and regular geometric form rotating with the support ill mounted to permit outward movement under the action of centrifugal force. means for establishing. a dclinite radius of rotation indicating that the center of mass is located at a predetermined 'adius, centripetal force mzans oppos-"ing the outward movement of the mass with centripetal force increasing with the outward moren'ient and means to establish measurable radius of rotation for the center of gravity of the mass: of the rotating body.

2. In a centrifugal instruction device. a rotating support, a mass of simple and reenlar geometric form rotating with the support and mounted to permit outward morement under the action of centrifugal force, centripetal force means opposing the outward movement of the mass with centripetal force increasing with the outward movement more rapidly than the centrifugal force increases at constant angular velocity.

3. In a. centrifugal instruction device, a rotating support. a mass of simple and regular geometric form rotatine with the support and mounted to permit. outward movement under the action (it centrifugal force, centripetal force means opposing: the outward movement of the mare: with centripetal force increzusiuc with the outward movement slightly more rapidly than the centrifugal force. increases at constant angular velocity.

loo

llll

4. In a centrifugal instruction device, a rotating support, a mass of simple and regular geometric form rotating with the support and mounted to permit outward movement under the action of centrifugal force means for establishing a definite radius of rotation indicating that the center of mass is located at a predetermined radius, a spring opposing the outward movement of the mass and means to establish measurable radius of rotation for the center of gravity of the mass of the rotating body.

5. In a centrifugal instruction device, a rotatin support, a mass rotating with the support and mounted to permit outward movement under the action of centrifugal force and a spring opposing the outward movement of the mass and having a constant OEMQF.

6. In a centrifugal instruction device, a rotating support, a mass of simple and regular geometric form rotating with the support and mounted to permit outward movement under the action of centrifugal force means for establishing a definite radius of rotation indicating that the center of mass is located at a predetermined radius, a helical spring operatively connected with the mass with its axis in line with the center of gravity of the mass and offering centripetal force to resist outward movement of the mass and means to establish measurable radius of rotation for the center of gravity of the mass of the rotating body.

7. In a centrifugal instruction device, a rotating support, a mass rotating with the support and mounted to permit outward movement under the action of centrifugal force and a helical spring operatively connected with the mass with its axis in line with the center of gravity of the mass and offering centripetal force to resist outward movement of the mass, said spring having a constant CMw'.

8. In a centrifugal instruction device, the combination of an oblong frame mounted to rotate about a vertical axis transverse to the length of the frame, a mass carried by the frame mounted to move outwardly with respect to the axis of rotation, a. helicalspring opposing the outward movement of the mass and having one end fixed to the frame and the other end operatively connected with the mass in line with the center of gravity, and means operated by the movement of the mass for indicating when the center of gravity of the mass is at a selected distance from the axis of rotation.

9. In a centrifugal instruction device, the

combination of an oblong support mounted to rotate about a vertical axis transverse to the support, means for indicating on the support the plane of the axis of rotation, a

mass carried by one end of the support and mounted to move outwardly'under the action of centrifugal force, means to indicate on the mass the plane of thecenter of gravity'thereof, a counter-weight carried by the 10. In a centrifugal instruction device, the

combination of a support mounted to rotate about a vertical axis transverse thereto, means to indicate on the support the plane of the axis of rotation, a mass carried by the support and mounted to permit outward movement under the action of centrifugal force, means on the mass to indicate the location of the center of gravity thereof, an index on the support in line with the axis of rotation and a pointer operated by the movement of the mass and having one end adjacent to the index.

11. In a centrifugal instruction device, the combination of a support mounted to rotate about a vertical axis, means to indicate on the support the plane of the axis of rotation, a mass pivotally mounted on the support on an axis at one side of the center of gravity of the mass and at one side of the axis of rotation of the mass, means to indicate on the mass the location of the center of gravity thereof, means for exerting increasing centripetal force upon the mass as it swings away from the axis of rotation, an index coaxial with the axis of rotation and a pointer operated by movement of the mass and having one end adjacent to the index.

12. In a centrifugal instruction device, the combination of anoblong frame including a top, a bottom, and ends connecting the top and bottom, a mass movably mounted onthe frame adjacent to one end and adapted to move outwardly under the action of centrifug'al force, a counter-weight mounted adjacent to the opposite end and tending to cre-' ate dynamic balance anda helical spring operatively connected with the support and the mass with its axis in line withthe center of gravityiof the mass.

13.111 a centrifugal instruction device, a rotating support, a mass rotating with the support and mounted to permit outward movement under the action of centrifugal force and a helical spring crossing the axis of rot-at1on and operatively connected with the mass with its axis in line with the center of gravity of the mass and offering centrip rotating support, a mass rotating with the support and mounted to permit outward movement under the action of centrifugal force and a helical spring operatively connected with the mass with its axis in line with the center of gravity of the mass and offering centripetal force to resist out-ward movement of the same said spring having a constant such that the centripetal. force at equilibrium is produced by an elongation of the spring nearly equal to the radius of rotation of the mass.

In testimony whereof I allix my signature.

PAUL E. KLOPSTEG. 

